GMB national construction secretary Phil Davies said Carillion had tried to force a shift system on the workers, including a night shift.
He said workers had been unhappy about signing the new contracts but had been warned by the company that failure to sign would lead to dismissal.
Davies said he had written to Carillion to warn the company that anybody signing the contracts would be doing so under duress.
In the letter, seen by Building, Davies said he understood workers had been informed that anyone submitting duress forms would be dismissed immediately. Davies made it clear he felt this to be intimidation.
The letter said: "The GMB view this as bullying and harassment of our members and are not prepared to stand for this type of behaviour from any employer."
It is understood that Carillion has presented the workers with three shifts: 5am to 1pm, 1pm to 9pm or 9pm to 5am. Carillion has argued that, based on advice from the Construction Federation, it is too late for grievance procedures.
Davies said: "This is the worst management I have ever dealt with. Carillion's policies fly in the face of the government's family-friendly working policies for workers and this situation is incredible, considering that this is a government highways contract." He added that he would be contacting government ministers to discuss the situation.
As Building went to press, the GMB was meeting to discuss plans for the timing of the strikes and preparing to give Carillion seven days' notice, as it is required to do by law.
A Carillion spokesperson said all the workers on the site had signed new contracts that had begun on Monday. She said: "Obviously we await any further information from the union, and our communication channels are always open."